GATE EC 2014 Set 4 — Question 17
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Question
The magnitude of current (in mA) through the resistor in the figure shown is_______.
Correct answer
2.79 to 2.81
Solution
To find the current through , we can use source transformation to simplify the circuit into a single loop.Step 1: Source Transformation
After transformation, the circuit is a single loop containing four resistors () and two voltage sources ( and ).
The current through the loop (which is the current through ) is given by Ohm's Law:The magnitude of the current through is .
- The left branch has a current source in parallel with . This can be transformed into a Thevenin equivalent voltage source: in series with . Since the current source points upwards, the positive terminal of the source is at the top.
- The right branch has a current source in parallel with . This can be transformed into a Thevenin equivalent voltage source: in series with . Since the current source points downwards, the positive terminal of the source is at the bottom.
After transformation, the circuit is a single loop containing four resistors () and two voltage sources ( and ).
- Total resistance in the loop: .
- Total voltage in the loop (tracing clockwise): The source and the source are additive in the clockwise direction. .
The current through the loop (which is the current through ) is given by Ohm's Law:The magnitude of the current through is .
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